• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Abnf
        • Deftreeops
        • Defdefparse
        • Defgrammar
        • Abnf-tree-utilities
        • Notation
          • Syntax-abstraction
          • Semantics
            • Tree-terminatedp
            • Tree->string
            • String-has-finite-parse-trees-p
            • Parse-trees-of-string-p
            • Tree-match-element-p
            • Parse-treep
            • Symbol
            • Nat-match-insensitive-char-p
            • String-unambiguousp
            • Tree-match-num-val-p
            • Nats-match-insensitive-chars-p
            • Tree-option
            • String-parsablep
            • Lookup-rulename
            • Nats-match-sensitive-chars-p
            • Numrep-match-repeat-range-p
            • Tree-match-char-val-p
            • Tree-list-match-repetition-p
            • String-ambiguousp
            • Nat-match-sensitive-char-p
            • Parse
            • Tree-match-prose-val-p
            • Theorems-about-terminated-trees-matching-elements
            • Tree-option-result
            • Tree-list-result
            • Tree-list-list-result
            • Tree-result
            • Tree-list-list-match-concatenation-p
            • Languagep
            • Terminal-string-for-rules-p
            • Tree-list-list-match-alternation-p
            • Tree-list-match-element-p
            • Parse!
            • String
            • Tree-set
            • Trees
          • Abstract-syntax
          • Core-rules
          • Concrete-syntax
        • Grammar-parser
        • Meta-circular-validation
        • Parsing-primitives-defresult
        • Parsing-primitives-seq
        • Operations
        • Examples
        • Differences-with-paper
        • Grammar-printer
        • Parsing-tools
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • Event-macros
      • C
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Std-extensions
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Semantics

Theorems-about-terminated-trees-matching-elements

Some theorems about terminated trees matching certain elements.

Definitions and Theorems

Theorem: tree-nonleaf-when-match-rulename/group/option

(defthm tree-nonleaf-when-match-rulename/group/option
  (implies (and (tree-match-element-p tree element rules)
                (member-eq (element-kind element)
                           '(:rulename :group :option))
                (tree-terminatedp tree))
           (equal (tree-kind tree) :nonleaf)))

Theorem: tree-leafterm-when-match-numval/charval

(defthm tree-leafterm-when-match-numval/charval
  (implies (and (tree-match-element-p tree element rules)
                (member-eq (element-kind element)
                           '(:num-val :char-val)))
           (equal (tree-kind tree) :leafterm)))

Theorem: tree-rulename-when-match-rulename

(defthm tree-rulename-when-match-rulename
  (implies (and (tree-match-element-p tree element rules)
                (element-case element :rulename)
                (tree-terminatedp tree))
           (equal (tree-nonleaf->rulename? tree)
                  (element-rulename->get element))))

Theorem: tree-branches-match-alt-when-match-rulename

(defthm tree-branches-match-alt-when-match-rulename
 (implies
   (and (tree-match-element-p tree element rules)
        (element-case element :rulename)
        (equal alt
               (lookup-rulename (element-rulename->get element)
                                rules))
        (tree-terminatedp tree))
   (tree-list-list-match-alternation-p (tree-nonleaf->branches tree)
                                       alt rules)))

Theorem: tree-nats-match-sensitive-when-match-char-val-sensitive

(defthm tree-nats-match-sensitive-when-match-char-val-sensitive
 (implies
  (and
   (tree-match-element-p tree element rules)
   (element-case element :char-val)
   (char-val-case (element-char-val->get element)
                  :sensitive)
   (equal
    chars
    (explode
        (char-val-sensitive->get (element-char-val->get element)))))
  (nats-match-sensitive-chars-p (tree-leafterm->get tree)
                                chars)))

Theorem: tree-nats-match-insensitive-when-match-char-val-insensitive

(defthm tree-nats-match-insensitive-when-match-char-val-insensitive
 (implies
  (and
   (tree-match-element-p tree element rules)
   (element-case element :char-val)
   (char-val-case (element-char-val->get element)
                  :insensitive)
   (equal
    chars
    (explode
      (char-val-insensitive->get (element-char-val->get element)))))
  (nats-match-insensitive-chars-p (tree-leafterm->get tree)
                                  chars)))